SIMULATION 

Metric weights and delay changes plus PBR setup on R3 is the way to go.
You have to put metric weights on all EIGRP routers (R3, R4, R5, and R6), not just a few, or adjacency will break-easy to miss. Also, both R4 and R6 Gi0/1 need delay 1000 so the backup path gets penalized. PBR config goes on R3 with proper ACLs and route-maps. I think some might forget the delay on both routers, but that's key. Agree?
Metric weights on all EIGRP routers, add delay 1000 to R4 and R6 Gi0/1, ACL and route maps for PBR on R3.
Shouldn't you also apply metric weights to every EIGRP router (R3, R4, R5, R6) so adjacency forms? Also, do both R4 and R6 Gi0/1 interfaces get the delay command for Task 2 or just one? Trying to be sure.
